The reaction is given by: 2 NO 2 ( g ) → N 2 O 4 ( g ) Given Δ U f ∘ [ N 2 O 4 ( g )] = 2 k c a l / m o l e and Δ U r ∘ e a c t i o n = − 16 k c a l / m o l . Calculate Δ H f ∘ or ma t

Question

The reaction is given by: 2 NO 2 ​ ( g ) → N 2 ​ O 4 ​ ( g ) Given Δ U f ∘ ​ [ N 2 ​ O 4 ​ ( g )] = 2 k c a l / m o l e and Δ U r ∘ ​ e a c t i o n = − 16 k c a l / m o l . Calculate Δ H f ∘ ​ or ma t i o n of NO 2 ​ (in kcal/mol) at 727 ℃.

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Question Explanation:

Calculate the standard enthalpy of formation of NO at a given temperature, given internal energy data for a related reaction and the internal energy of formation of NO.

Concept:

The question is based on the relation between $Δ H$ and $Δ U$ and Hess's Law.

Solution:

The reaction is:

$2 N O_{2} (g) \to N_{2} O_{4} (g)$

Given:

$- 16 = 2 - 2Δ U_{f}^{\circ} [N O_{2} (g)]$

$Δ U_{f}^{\circ} [N O_{2} (g)] = 9 k c a l / m o l$

For the formation of $N O_{2}$ :

$\frac{1}{2} N_{2} (g) + O_{2} (g) \to N O_{2} (g)$

The relationship between enthalpy and internal energy is:

$Δ H_{f}^{\circ} = Δ U_{f}^{\circ} + Δ n_{g} RT$

Here, $Δ n_{g} = 1 - (0.5 + 1) = 1 - 1.5 = - 0.5$

So,

$Δ H_{f}^{\circ} [N O_{2} (g)] = 9 - \frac{1}{2} (\frac{2}{1000}) (1000)$

$Δ H_{f}^{\circ} [N O_{2} (g)] = 9 - 1 = 8 k c a l / m o l$

Final Answer: 8

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